This is an old question, and I'm sorry for that, but I am happy to answer. The first thing you should have done is ask whether you were free to leave, or whether you were being arrested. If you were not free to leave, you are entitled to an attorney's presence during questioning, which you should ALWAYS request. Never speak to the police without an attorney present. If you can't afford one, the police can provide you a public defender.
Getting to your question about he said/she said: is it possible to have charges filed against you when there is no physical evidence of an incident, and the only evidence is the word of a witness? Yes. Can the government pursue this case even when you have made statements that contradict the witness' statement? Yes. Could you be convicted on the basis of her word alone? Yes. You need to work with an attorney to find out all the inconsistencies in her report, how you can show she lied to police, and how the government cannot prove its case beyond a reasonable doubt. I hope this turned out okay for you and you were able to get the legal assistance you needed.